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## Mathematics of transverse isotropy with a horizontal axis of symmetry

The elastic modulus matrix of an HTI medium with a symmetry axis along the x direction (which I will denote as ) has the following form (in compressed notation):

 (3)
This representation can easily be obtained by a rotation of the VTI's elastic matrix along the y axis. Incorporating this expression into equation (1) and identifying as the velocity of the plane wave with propagation direction (kx,ky,kz) gives us

 (4)

From here on, to simplify notation, I use the variables and , introduced by Dellinger 1991. Thus we rewrite equation (4) as

 (5)

 HTIprop Figure 1 Definition of propagation angles. The azimuthal angle is measured with respect to the symmetry axis, and the incidence angle with respect to the vertical axis.

Next: Plane wave modes Up: TRANSVERSE ISOTROPY Previous: TRANSVERSE ISOTROPY
Stanford Exploration Project
11/12/1997